I apologize for the automatic translation.
Hello everybody. I recently started writing a small script that allows you to do Bevel after the Booleans. I just started learning Python and Blender api. Therefore, my implementation is very primitive and contains errors.
My code may look very bad and contain many errors. But I’ll try to fix it in the future.

To use, Tools Panel>Boolean Bevel.

Description of functions:
Show wire - Displays and hides the wire
Change Boolean Operation - Allows you to change Boolean operations (Union, Difference, Intersect и Slice)
Change subdivide - If objects have Subsurf, then it can be changed (for each one separately). Take the last modifier Subsurf
Simplify - Simplifies the intersection
Subdivide Patch - Subdivides the intersection
Relax - Smooths the intersection
Cut radius - Bevel radius
Sides of circle - The number of faces of the curve (the object is cut differently)
Fix Curve Twist - Must correct the twist of the curve (does not always work)
Mean Tilt - Mean Tilt of curve (for differently cut object)
Twist Mode - Mode of twist curve.
Preview Curve - Preview the curve, before the cut. (In the future for the variable fillet). Now you can check the self-intersection of the curve.
Path Operation - (The object is cut differently). Union works better.
Fillet Profile - Bevel’s profile (it’s better to change from the modifier)
Fillet Segments - Number of segments Bevel (better to change from the modifier)
Smooth - corrects twisting of a curve
Split Ngon - Triangulate NGon
Method - Triangulate method
Fix Bevel - removes the interfering edges
Sharp - If there are sharp edges on the intersection
Remove Vertex - Removes nearby vertices
Interpolation - relax interpolation
Smooth Bevel - Bevel smoothing with the strength and number of nearest vertices
Use material - assignment of materials to the object (Bevel, source object and boolean object)
Custom Normals - use custom normals for good reflections.
Make Pipe - create pipe on intesection.

For Variable Radius:

In the Add-on you need to select Preview Curve.

Then you need to enter the curve editing mode.

Perform the necessary actions. Let’s choose a point in proportional editing and change its radius (Alt + S).

Warning: This add-on is still in development. Badly works with low-poly objects.

Edit 29.08.2017: Update file (Now the shape of the transition, should be more smooth.).
Edit 01.09.2017:
Add presets
Add stop calculation button - Stop the script execution in order to change settings faster
Create bevel - You can not create Bevel
Remove Objects - remove all guides and curves which were created by the add-on
Apply Modifiers - apply all modifiers or modifiers which were created by the add-on on selected objects
Remove Modifiers - remove all modifiers or modifiers which were created by the add-on on selected objects
Edit 19.09.2017
Fix Custom Edge and Custom Normal
Add Symmetrize
Edit 28.09.2017
Add Make Pipe
05.10.2017
‘Make Pipe’ works with custom Edge
Added Remove Pipes
Something else that I do not remember.

Because the ‘bevel’ applied by this addon looks like a second mesh applied to the target/boolean-ed mesh (then joined both together). What I say is right?
I mean, the ‘bevel’ mesh of this addon simulate the shape of blender’s bevel, but how that shape is made exactly? It take the information of that shape from the already present blender’s bevel, or you writed in the addon code the ‘position’ of the various verts to obtain that shape? If the latter, then you can add ‘positions’ to obtain more/various bevel shapes. Sorry Rodinkov my english is not good too; btw can you explain that aspect?

Because the ‘bevel’ applied by this addon looks like a second mesh applied to the target/boolean-ed mesh (then joined both together). What I say is right?
I mean, the ‘bevel’ mesh of this addon simulate the shape of blender’s bevel, but how that shape is made exactly? It take the information of that shape from the already present blender’s bevel, or you writed in the addon code the ‘position’ of the various verts to obtain that shape? If the latter, then you can add ‘positions’ to obtain more/various bevel shapes. Sorry Rodinkov my english is not good too; btw can you explain that aspect?